Publication: Backtesting expected shortfall: accounting for tail risk
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2016-03-10
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INFORMS
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Abstract
The Basel Committee on Banking Supervision (BIS) has recently sanctionedexpected shortfall (ES) as the market risk measure to be used for banking regulatorypurposes, replacing the well-known value at risk (VaR). This change is motivated by theappealing theoretical properties of ES as a measure of risk and the poor properties ofVaR. In particular, VaR fails to control for “tail risk.” In this transition, the major challengefaced by financial institutions is the unavailability of simple tools for evaluation of ESforecasts (i.e., backtesting ES). The main purpose of this paper is to propose such tools.Specifically, we propose backtests for ES based on cumulative violations, which are thenatural analogue of the commonly used backtests for VaR. We establish the asymptoticproperties of the tests, and investigate their finite sample performance through someMonte Carlo simulations. An empirical application to three major stock indexes showsthat VaR is generally unresponsive to extreme events such as those experienced duringthe recent financial crisis, whereas ES provides a more accurate description of the riskinvolved.
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Risk management, Expected shortfall, Backtesting, Tail risk, Value at risk
Bibliographic citation
Du, Z., & Escanciano, J. C. (2017). Backtesting Expected Shortfall: Accounting for Tail Risk. Management Science, 63 (4), pp. 940-958.